Plasma blobs in a basic toroidal experiment - CRPP www - EPFL

PHYSICS OF PLASMAS 14, 110704 共2007兲

Plasma blobs in a basic toroidal experiment: Origin, dynamics, and induced transport S. H. Müller,a兲 A. Diallo, A. Fasoli, I. Furno, B. Labit, and M. Podestà Centre de Recherches en Physique des Plasmas (CRPP)—Association Euratom-Confédération Suisse, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

共Received 20 August 2007; accepted 25 October 2007; published online 28 November 2007兲 Detaching plasma blobs with very similar properties to tokamaks are observed in the basic toroidal plasma experiment TORPEX 关A. Fasoli et al., Phys. Plasmas 13, 055902 共2006兲兴. The blobs originate from the breaking of wave crests of a drift-interchange wave, which span over regions characterized by strongly inhomogeneous background parameters. Once decoupled from the wave, the blobs follow a predominantly radial trajectory pattern. The blob-induced cross-field transport can instantaneously exceed the steady-state parallel fluxes by one order of magnitude, while accounting for only 10% of the time-average device losses. If the particles were confined in the parallel direction, as is the case in tokamaks, blobs would constitute the dominant loss mechanism in TORPEX. The presented results show that the presence of grad B is sufficient and neither a magnetic-topology change nor the presence of limiters, both absent in TORPEX, are necessary for the generation of blobs. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2813193兴 The study of plasma blobs, i.e., intermittently encountered, isolated propagating structures of increased plasma density, is one of the most active research areas in tokamak edge plasma physics, as blobs are believed to dominate the transport across the scrape-off layer 共SOL兲 and possibly lead to localized wall loads that may become critical for ITER.1 Extensive experimental data have been gathered on tokamaks 共Refs. 2–5, and references therein兲, stellarators,5,6 and reversed-field pinches,7 using measurements of the visible light emission of neutrals in contact with the plasma, imaged by fast cameras3,6 or other detector arrays,2,7 and from Langmuir probe 共LP兲 measurements in the SOL.4,5 These data universally show pronounced non-Gaussian features in timeseries probability distribution functions2,4,5,7 共PDFs兲 and radial blob propagation velocities of about 1 km/ s.2,6,8 The blob observation patterns in low- and high-confinement modes vary significantly,3,6 highlighting their importance as clues towards an understanding of fundamental aspects of the tokamak edge plasma. Extensive theoretical work on the ejection 共Refs. 9 and 10, and references therein兲 and propagation mechanisms 共Refs. 10–12, and references therein兲 of blobs has been motivated by the experimental observations. Recent numerical simulations show that blobs can originate from drift-interchange turbulence,4,9 finding agreement with LP data of the tokamak à configuration variable 共TCV兲 in several aspects.4 Linear devices have reported events with a radial propagation component, similar to tokamak observations in terms of statistical properties and absolute velocities 共Refs. 13–15, and references therein兲. Both detached 共bloblike兲13,14 and nondetached 共fingerlike兲15 structures have been observed in different linear configurations. In this Letter, we report the observation of blobs in the basic toroidal plasma experiment TORPEX 共major radius R = 1 m, minor radius a = 0.2 m兲.16 We show that blobs with very similar properties to tokamaks detach from wave crests a兲

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of a drift-interchange wave, even in the absence of both a magnetic-topology change and limiters. The experimental setup is achieved by limiting the rf plasma production to a region on the high-field side by using a low toroidal magnetic field of B␸ = 76.6 mT on axis and an injected rf power of ⬃300 W, very low compared to Ref. 16 共helium neutral gas pressure pn = 2.5⫻ 10−5 mbar兲. The electron cyclotron 共EC兲 resonance lies thus at r ⯝ −12 cm, where r is the coordinate along the major radius, with r = 0 at the minor axis. The low rf power translates into low densities 共n ⱗ 7 ⫻ 1016 m−3兲; therefore, the upper-hybrid and EC resonance layers are relatively close to each other.17 No rf plasma production is present in the region r ⲏ 0, which is therefore referred to as the SOL region, driven by fluxes from the core region at r ⱗ 0. The confinement scheme employs a vertical magnetic-field component,18 which connects all field lines to the wall 共Bz = 1.6 mT; maximum three helical turns or 20 m connection length兲. Electron temperature and plasma potential in TORPEX generally lie in the range of Te ⬃ 3 – 8 eV and V p ⬃ 10– 20 V. Other relevant parameters are cs ei en ⬃ 104 m / s, ␳s ⬅ cs / ␻ci ⬃ 2.5 mm, ␭mfp ⬃ ␭mfp = O共1 m兲, and parallel correlation length L储⬃ several meters. The analysis presented in the following is based on three discharge records of 0.6 s length each 共total length: 450 000 time frames兲 of the two-dimensional LP array HEXTIP 共hexagonal turbulence imaging probe兲.19 The data are low-pass filtered at 30 kHz to cutoff fluctuations outside the HEXTIP bandwidth. The construction of HEXTIP implements several features to minimize perturbations of the plasma19 and no features related to its presence are generally found in other probe signals. Figure 1共a兲 compares two simultaneous time-series samples, taken at the core-SOL transition and in the far SOL, respectively. While the former shows coherent oscillations at a frequency of 共14.9± 1.8兲 kHz, the latter is characterized by rare and irregular bursts. The conditionally averaged waveforms4,20 are shown in Fig. 1共b兲, triggered when the

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FIG. 1. 共Color online兲 共a兲 Two raw time-series samples. 共b兲 Conditional waveforms triggered when the signal “䉭” exceeds the level indicated in 共a兲. Inset: probe positions relative to the density profile 共contours at 兵1.9, 3.85, 5.8其 ⫻ 1016 m−3兲.

density fluctuations in the outer SOL exceed the level indicated in Fig. 1共a兲. An event in the far SOL is preceded statistically about 0.15 ms earlier by a surplus density at the core-SOL transition, which then propagates radially. This compares closely to the signatures of blobs in tokamaks, including the asymmetric conditional waveforms in the SOL.4 In order to understand the origin of the blobs, we investigate the oscillations at the core-SOL transition more closely. Figure 2 shows that the oscillations correspond to a strong coherent wave with wavelength ␭z = 共13.6± 1.0兲 cm, or 共54± 4兲␳s, which propagates vertically upward along the core-SOL transition with a velocity of 共2000± 250兲 m / s, or 共0.2± 0.025兲cs, inferred from wave-crest tracking after filtering the HEXTIP data in the wave spectral region. Such waves have been identified as drift-interchange waves on TORPEX, which, in the present limit of high Bz, assume a dominant interchange character with k储 ⬇ 0.16,21 The measured vertical wavelength agrees with the value dictated by k储 ⬇ 0; namely, ␭z共r = 0兲 = 2␲R共Bz / B␸兲 ⯝ 13.1 cm. We observe that the emergence of blobs is closely related to the nonlinear dynamics of wave crests of the driftinterchange wave. Figure 3 shows six movie frames of the density fluctuations, representative of a typical sequence leading to the ejection of a blob. A large wave crest in the center 共frames 1–2兲 elongates radially and deforms 共frames 3–4兲. While the central part of the wave crest continues to move on at the wave velocity, the outer part spans into a

FIG. 2. 共Color online兲 共a兲 Relative area underneath the highest spectral peak centered within the frequency interval of 关13.1, 16.7兴 kHz, as a function of position in the rz plane. 共b兲 Snapshot of the spatial wave pattern corresponding to this frequency region.

FIG. 3. 共Color online兲 Density-fluctuation movie frames, separated by 6 ␮s, showing the ejection of a blob.

region characterized by very different background parameters, in which it disperses differently 共frames 4–5兲. The outer part increasingly lags behind until the wave crest breaks apart 共frame 5–6兲. The resulting isolated region of high plasma density in the SOL region represents a newborn blob, which completely detaches from the core region 共frame 6兲. Due to the inherently turbulent nature of the blobs, a probabilistic framework must be adopted to capture their dynamical properties. In the following, we apply a patternrecognition approach combined with statistical analysis,22 which identifies and tracks positive and negative structures, defined as regions where ␦n ⭵ ± ␦nth, respectively. The threshold value ␦nth is chosen as in Ref. 22 as the standard deviation of the concatenation of all average-subtracted density signals, and is the same as in Fig. 1. Only structure trajectories lasting longer than 0.12 ms are considered in the statistical analysis. Figure 4 shows the trajectory histograms and the average structure velocity field22 for positive and negative structures as well as the profile of the time-series skewness S. In the center of the wave region, where S ⯝ 0 – 0.5, the trajectory patterns for positive and negative structures are very similar, while in the SOL region only positive structures—the blobs—have a significant probability of occurrence. The blob trajectories bend from the vertical wave corridor and propagate mainly radially in the SOL. The asymmetry in the macroscopic structures is also manifest in the time-series PDFs. The skewness is negative in the core region 共S ⯝ −1兲, indicating the presence of negative bursts, shows a strong gradi-

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FIG. 4. 共Color online兲 Trajectory histogram for positive 共a兲 and negative 共b兲 structures. 共c兲 Time-series skewness. 共d兲 PDFs.

ent over the core-SOL transition and stagnates at values of S ⯝ 1 – 1.5 in the SOL 关Fig. 4共c兲兴. This closely resembles measurements of skewness profiles across the separatrix in tokamaks2 and corresponding observations in linear devices.13 Figure 4共d兲 shows the full PDFs of the standardized density ␦n / ␴n at four radial positions. The PDFs change from negatively to positively skewed double-humped types over the wave region and show the familiar universal shape in the SOL.23 The pilot chart22 in Fig. 5 confirms the turbulent nature of structure motion by showing significant spreads in the propagation-direction probabilities. The highest probabilities agree with the mean flow field in Fig. 4共a兲. The average radial velocities along the blob trajectories decrease from 1750 m / s 共0.175cs兲 to 1000 m / s 共0.1cs兲, consistent with tokamak observations.2,8 Changes in the average structure orientation and aspect ratio are also evident, along with a decrease of the average blob sizes.

FIG. 5. 共Color online兲 Pilot chart for positive structures. Each “rose” symbol represents the statistical structure properties in the surrounding squareshaped region. Length of arrow shafts ⬀ probability of direction; number of feathers: Average speed in multiples of 250 m / s; area of central circle ⬀ number of structures; “L” symbols: Average structure orientation and extension.

The transport properties of the blobs are investigated in Fig. 6, following Ref. 22. The ensemble-averaged structure¯ 典 ⬅ 具␦nv典 共␦n is the structureinduced flux-density field 具⌫ averaged excess density, v the structure velocity, and 具·典 an ensemble average over all realizations of positive and negative structures兲 shows that almost no vertical net flux exists in the wave region; the contributions of different signs cancel. A radial net flux-density field, caused by the blobs, domi¯ 典⯝3 nates the SOL region, reaching values of 具⌫ r 19 −2 −1 ⫻ 10 m s . Note that this value characterizes the average instantaneous transport during blob events, and that their time-average effect is expected to be much lower. The latter is estimated in Fig. 6, by counting the number of particles per unit area traversing a grid of radial test surfaces over an observation time ␶, and dividing by ␶. The time-average blob-induced transport obtained in this way reaches values up to 具⌫r典␶ ⯝ 7 ⫻ 1017 m−2 s−1, highest on the equatorial plane close to the ejection region. To bring the measured values into a quantitative context, we note that the steady-state losses in the present configuration are dominated by the pro-

FIG. 6. 共Color online兲 Time-average structure-induced radial transport at ¯ 典, the average instantaneous transdifferent locations. The arrows show 具⌫ port during events.

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jected parallel fluxes ⌫z ⬇ 21 ncs共Bz / B␸兲 ⬇ 5 ⫻ 1018 m−2 s−1.18 Estimating the effective loss areas to be roughly equal 共blobs: outboard side of the core plasma; parallel losses: top and bottom sides兲, the blobs thus account for only 10% of the time-average device losses, but can induce fluxes of typically 10⫻ ⌫z during events. If the particles were confined in the parallel direction, as is the case in tokamaks, blobs would constitute the dominant loss channel. Finally, the presented results suggest that wave-breaking might be a suitable framework to understand the formation of blobs in TORPEX, supported by the observation that, before blobs break off, wave crests first span far into the SOL region where they completely dominate the background plasma density 共see Fig. 3兲. In such a case, it is likely that the wave propagation is no longer governed by background plasma parameters, but by the properties of the wave crests themselves. Such nonlinearities in the wave propagation may lead to wave-breaking, which could be a possible mechanism for the formation of blobs. However, the full dynamics of the wave-blob system is very complicated, and by far not all blobs fit into the same pattern, so it remains a great challenge to uncover the correct picture of blob formation, which is subject to intense ongoing research. In summary, it has been demonstrated that detaching plasma blobs with very similar properties to tokamaks exist in a basic toroidal configuration, allowing the conclusion that ⵱B forces are sufficient and neither a magnetic-topology change nor the presence of limiters are necessary prerequisites for the formation of blobs. In TORPEX, the blobs result from wave crests of a drift-interchange wave. A similar relation between coherent modes and bursty events has been found in linear devices.14,15 This observation in basic devices may motivate specific research for a relation between edge oscillations and blobs in tokamaks, for which no such relation has been characterized as yet. The presented quantitative analysis of the blob-induced transport suggests that blobs constitute the dominant cross-field particle-loss mechanism in TORPEX, confirming their critical role for closed fieldline configurations. Due to the satisfaction of the fundamental assumptions of leading blob theories, in particular, the

presence of ⵱B forces, the simplicity of the configuration, and the availability of extensive experimental information, the presented case may prove very useful for the validation of theoretical models and numerical simulations of blobs. S.H.M. gratefully acknowledges fruitful discussions with T. A. Carter, P. H. Diamond, and G. R. Tynan. This work is partly supported by the Fonds National Suisse de la Recherche Scientifique. 1

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